derivation of s= u+ 1/2 at2​

Answers

Answer 1

We know that

Velocity is given by the rate of change of position w.r.t time

[tex]\\ \sf\longmapsto v=\dfrac{dx}{dt}[/tex]

[tex]\\ \sf\longmapsto vdt=dx[/tex]

Now we can see in above v is not independent of t .So we replace the value of v by v=u+at and we get

[tex]\\ \sf\longmapsto (u+at)dt=dx[/tex]

Integrate with limits 0 to t and x_o to x respectively .

[tex]\\ \sf\longmapsto u{\displaystyle{\int}_0^t}dt+a{\displaystyle{\int}_0^t}dt={\displaystyle{\int}^x_{x_0}}dx[/tex]

[tex]\\ \sf\longmapsto ut+\dfrac{1}{2}at^2=(x-x_0)[/tex]

[tex]\\ \sf\longmapsto x=x_0+ut+\dfrac{1}{2}at^2[/tex]


Related Questions

PLZ FAST Scientific knowledge is both long lasting and always _______.

changing
non-observable
permanent
untestable

Answers

The answer is changing

ecent communication with the inhabitants of Neptune has revealed that they have a Celsius-type temperature scale, but based on the melting point (0oN) and boiling point (100oN) of their most common substance, hydrogen. Further communications have revealed that the Neptunians know about perfect gas behavior and they find that, in the limit of zero pressure, the value of pV is 28 dm3atm at 0oN and 40 dm3atm at 100oN. What is the value of the absolute zero of temperature on their temperature scale

Answers

The absolute zero temperature is the smallest thermodynamic thermal limit, which is considered as a zero kelvin when the enthalpy, as well as the entropy of a cooled ideal gas, are of minimal value.

It is expressed by using the formula:

[tex]\mathbf{T_{abs} = T_N + k}[/tex]

where;

[tex]\mathbf{T_{abs } = absoulte \ temperature}[/tex]

[tex]\mathbf{T_N = temperature \ at \Neptune \ Scale}[/tex]

k = factor to convert temperature from absolute scale to Neptunian scale

N:B: An absolute temperature = zero (0) kelvin

From the information given, Using Ideal gas since it is used in Neptune:

PV = nRT

where;

P = pressureV = volumen = no of molesR = rate(constant)T = temperature

From the question, provided that the gas is the same and no new mass is added;

Then, we can equate the moles of gas in the given conditions as;

[tex]\mathbf{\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}....\dfrac{P_nV_n}{T_n}}[/tex]

Using:

[tex]\mathbf{\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}}[/tex]

where the value of;

P₁V₁ = 28 dm³ atm

T₁ = 0⁰ N

P₂V₂ = 40dm³ atm

T₂ =  100⁰ N

[tex]\mathbf{\dfrac{28}{(0+K)}=\dfrac{40}{(K+100)}}[/tex]

By cross multiply;

28(K+100) = 40(0+K)

28K + 2800  = 0 + 40K

40K - 28K = 2800

12 K = 2800

K = 2800/12

K = 233.33° N

Recall that:

[tex]\mathbf{T_{abs} = T_N + k}[/tex]

[tex]\mathbf{0= T_N+ 233.33 ^0 N}[/tex]

[tex]\mathbf{ T_N= - 233.33 ^0 N}[/tex]

Therefore, we can conclude that the value of the absolute zero of temperature on their temperature scale is -233.33° N

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A sample of oxygen gas occupies a volume of 200 mL at a pressure of 720 torr. What volume will the gas occupy at a pressure of 800 torr if temperature is held constant

Answers

We have that the gas will occupy at a pressure of 800 torr if temperature is held constant a Volume of

[tex]V_2=0.18L[/tex]

From the Question we are told that

Initial Pressure [tex]P_1=720[/tex]

final Volume  [tex]V_1=200mL[/tex]

Initial Pressure [tex]P_2=800[/tex]

final Volume  [tex]V_2=?[/tex]

Generally the equation for Boyle's law  is mathematically given as

[tex]P_1V_1= P_2V_2[/tex]

Therefore

[tex]V_2=\frac{ P_1V_1}{P_2}\\\\V_2=\frac{ 720*200}{800}\\\\V_2=180mL[/tex]

[tex]V_2=0.18L[/tex]

The gas will occupy at a pressure of 800 torr if temperature is held constant a Volume of

[tex]V_2=0.18L[/tex]

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PLS FAST WILL GIVE BRAINLIEST Describe why atoms can be neutral when they contain charged subatomic particles.

Answers

Answer:

Atoms are neutral if they have the same number of charged protons and electrons, balancing positive and negative charges. As long as the numbers of electron and protons are the same, the charges will balance.

A car starts from rest and after 10 seconds its velocity is 20 m/s. Find the acceleration and the distance travelled by it.​

Answers

Answer:

a=[tex]2ms^{-2}[/tex]   S=100m

Explanation:

a=?

vi=0m/s

vf=20m/s

t=10s

a=[tex]\frac{vf-vi}{t}[/tex]

a=[tex]\frac{20-0}{10}[/tex]

a=2m[tex]s^{-2}[/tex]

S=?

S=vit+[tex]\frac{1}{2}[/tex]a[tex]t^{2}[/tex]

S=0+[tex]\frac{1}{2}[/tex]*2*[tex](10)^{2}[/tex]

S=100m

will mark brainliest!

Answers

Answer:

b=t-p(m-n)/s

Explanation:

y UD Eda
NF-22
11. A race car traveling at +44 m/s is uniformly accelerated to a velocity of +22 m/s over an
11-s interval. What is its displacement during this time?
a

Answers

We have to find acceleration first.

Initial velocity=u=44m/sFinal velocity=v=22m/sTime=11s=t

[tex]\boxed{\sf Acceleration=\dfrac{v-u}{t}}[/tex]

[tex]\\ \sf\longmapsto Acceleration=\dfrac{22-44}{11}[/tex]

[tex]\\ \sf\longmapsto Acceleration=\dfrac{-22}{11}[/tex]

[tex]\\ \sf\longmapsto Acceleration=-2m/s^2[/tex]

Now Distance=s

Using second equation of kinematics

[tex]\boxed{\sf s=ut+\dfrac{1}{2}at^2}[/tex]

[tex]\\ \sf\longmapsto s=44(11)+\dfrac{1}{2}(-2)(11)^2[/tex]

[tex]\\ \sf\longmapsto s=484+(-1)(121)[/tex]

[tex]\\ \sf\longmapsto s=484-(121)[/tex]

[tex]\\ \sf\longmapsto s=363m[/tex]

Explanation:

[tex]we \: want \: to \: find \: displacement \\ we \: can \: use \: newtons \: laws \: of \: motion \\ s = ut + \frac{1}{2} a {t}^{2}....(1) \\here \: 44 = u \: (initial) \\ v = 22(final) \\ t = 11 \\ then \: \\ s = 44 \times 11 + \frac{1}{2} (\frac{22 - 44}{11} ) {11}^{2} \\ s = 484 + \frac{1}{2} \times \frac{ - 22}{11} \times 11 \times 11 \\ s = 484 - 121 \\ s = 363m \\ thank \: you[/tex]

According to the law of conservation of energy, which statement must be
true?
A. Energy that is transformed is neither destroyed nor created.
B. Energy can change only from nuclear to chemical.
C. There is only one form of energy.
D. The total energy in a system can only increase over time.

Answers

Answer:

i hope it will help you

THANK YOU

Explanation:

thank you

scientist use empirical evidence, logical thinking, and tests to ___ a scientific explanation.​

Answers

Answer:

Explanation:

The only word I can think of is confirm.

I choose confirm because they have already used empirical evidence (evidence that is primarily found by the senses. We hear something, we see something, We smell something -- although this is rather rare. Probably we would hear or see something first). We've used logical thinking, and we've likely even performed experiments.

So we've done all the ground work. All of these things are needed to confirm a scientific thought or premise that has been proposed. All of them aim at confirming what  we proposed.

identify two ways in which friction is not useful in science​

Answers

Answer:

Friction between brakes and the wheels of a car or bicycle helps the vehicles slow down.If you do not lubricate your bike regularly with oil, the friction in the chain and axles increases.

What is the car’s average velocity (slope) between “O” and “A”? (y2-y1 / x2-x1) = slope
(1,24) (0,0)

Answers

Please find the attached photograph for your answer. Hope it helps! Please do comment

The car’s average velocity is mathematically given as

V=4m/s

What is average velocity?

Average velocity is simply the mean rate of change of position of a car over a period of different times and this can be used to attain velocity of a car that has been in different velocity states

What is the car’s average velocity?

Generally, the equation for the Velocity   is mathematically given as

V=(AI/OI)

Therefore

V=24/1

V=4m/s

In conclusion, the car’s average velocity

V=4m/s

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Which unit is used to measure the mass of a computer?

Answers

Answer:

kilogram

Explanation:

computers are measured in kilograms

calculate the frequency and time period of sound wave of 35 m wave length propagating at a speed of 3500m/s​

Answers

Answer:

Frequency = 100 Hz

Time period = 0.01 sec

Explanation:

f= 3500/35 = 100

T = 1/f = .01

PLSS HELP NOWW!!!!!!(01.01 LC) Which is an example of the force of attraction between two objects that have mass? (2 points) a Magnetism b Gravity c Solar energy d Electricity

Answers

Answer:

pretty sure it is gravity

Answer:

Electricity

Explanation:

Write about any 8 areas of field where physics  is applied .Illustrate  it with examples .​

Answers

Explanation:

In construction.When constructing roads, buildingIn Engineering, when engineering we use physics such as calculations.At homeIn industries, industries use chemicals and so on.In tailoring, we use the knowledge of physics like when sowing.In carpentry, we use calculations.In Hospitals, we use physics we balancing In Sites, we use energy.

Physics is a discipline that its applications cut across all fields. Ranging from banking, cooking, transportation, lecturing, medicine, engineering etc. It is the bed rock of engineering because all aspect of engineering involves the application of Physics.

Some of the fields where Physics is applied are:

a) Lecturing: This field requires the continuous dissemination of Physics knowledge to students from one level to another level.

b) Medicine: The various applications of physics in medicine can not be over-emphasized. This is because medicine involves the use of ultrasound, ionizing and non-ionizing radiation, magnetic resonance etc.

c) Electrical Engineering: In this field, the basic knowledge of Physics is applied to circuits, boards and electrical components.

d) Civil Engineering: The knowledge of stress, strain, shear, force, torque, weight etc are used in a lot of deductions.

e) Broadcasting station: This field make use of a lot of Physics principles so as to increase awareness and pass information. Thus the frequency of a broadcasting station determines her area coverage.

f) Transportation: As all vehicles consists of electrical devices, then the knowledge of Physics can bot be avoided.

g) Communication: Ranging from GPS, GPRS, Data transmission, voice call, email etc requires the knowledge and application of Physics.

h) Archaeology: Though not a related to Physics, but it requires the application of it. Radio-dating and carbon-dating are required to determine the age of some ancestral objects or artifacts.

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The motion of the particles is most orderly in

Answers

Answer:

Solids

Explanation:

Particles are most orderly in solids.

Help me with this quesiton

Answers

it takes him 1.2 hrs

Define acceleration. Prove that v = u + at​

Answers

Explanation:

[tex]\text{Acceration is the rate of change of velocity per unit time.}

\text{Suppose the initial velocity is }u,\text{ and the final velocity is }v.

\text{Then the change of speed is }v-u.

\text{If such velocity change takes }t\text{ seconds, the average acceleration is }a.

\text{So we write}[/tex]

[tex]\frac{v-u}{t}=a\implies v=u+at[/tex]

why does sound not transmit in vacuum

Answers

Answer:

because sound needs medium to transmit.

The sound is produced by vibration and if there is no medium there is no vibration and no vibration means no sound.

how do you measure the volume of irregular object? explain with diagram​

Answers

Answer:

by using graphical meythod

help me please i dont understand

Answers

Answer:

0.58

Explanation:

Sinẞ = opposite ÷ hypotenuse

Sinẞ = 5 ÷ 8.6

Sinẞ = 0.5814

Sinẞ ≈ 0.58

Answer:    0.58

Explanation:

hope this helps

Fun Fact: Peanuts aren’t technically nuts

The digital payment system that enables sellers to accept payment at trade
shows, food trucks, concerts, or farm stalls is called a:
A. biometric authentication system.
O B. QR code.
O c. payment protection device.
D. mobile point-of-sale device.
SUBMIT

Answers

[tex] \large \mathfrak{Answer : }[/tex]

The Correct option is D. mobile point-of- sale device.

The digital payment system that enables sellers to accept payment at trade shows, food trucks, concerts, or farm stalls is called a mobile point-of-sale device. Thus, the correct option for this question is D.

What are the advantages of a digital payment system?

The advantages of a digital payment system are as follows:

This type of payment system is cost and time-saving.It increases sales by reducing transaction costs.It is helpful in generating the invoice at any time.This mode of payment is paperless.

The mobile point-of-sale device (mPOS) is cost-effective. It involves the breaking down of monthly maintenance and payments on the basis of a cloud-based subscription. It authorizes the sellers to accept the payment at trade. It is one of the fastest modes of payment.

Therefore, a mobile point-of-sale device is a digital payment system that enables sellers to accept payment at trade shows, food trucks, concerts, or farm stalls. Thus, the correct option for this question is D.

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Why is the perfect mechine is not possible in the real life?​

Answers

Answer:

Because the mechanical advantage of the machine is affected by friction and weight but velocity ratio is not. So, mechanical advantage is less than velocity rate. Thus, the machine's efficiency is less than 100% and can't be a perfect machine

How does the field of science gain knowledge and understanding?

Answers

A basic question about how science gains knowledge.

Science gains knowledge using the scientific method.

The first thing you need to understand here is the scientific method, with all the steps and a little explanation to each one.

Ask a question or find some problem to solve: (what you want to understand? In what area do you want to find new knowledge?) Perform research: (There is some existing knowledge in that topic?) Establish your hypothesis: (This is what you can conclude with the things you know, or what you expect to find) Test your hypothesis by conducting an experiment: (Perform an experiment to test your hypothesis, this is the most important part.) Make an observation: (Observe the outcome of the experiment) Analyze the results and draw a conclusion: (study what the outcome means) Present the findings: (Present what you learned to the scientific community, in this way the science gains knowledge).

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Answer:

Through the testing of hypotheses.

which unit of measure is the correct SIunit to use in measuring the mass of a boulder?

o tons
o kilograms
o pounds
o ounces​

Answers

The correct answer is kilograms

Answer:

tons

Explanation:

will mark brainliest!

Answers

Answer:

Explanation:

Fa - u*m*g = m*a

Fa = u*m*g + m*a

Fa - m*a = u*m*g

u = [tex]\frac{Fa - m*a}{m*g}[/tex]

A 2.72 A current flows through a wire for
9.88 s. How much charge flows past a point
in the wire in that time?

Answers

Current=2.72A=ITime=t=9.88sCharge=Q

[tex]\\ \rm\longmapsto I=\dfrac{Q}{t}[/tex]

[tex]\\ \rm\longmapsto Q=It[/tex]

[tex]\\ \rm\longmapsto Q=2.72\times 9.88[/tex]

[tex]\\ \rm\longmapsto Q=26.87C[/tex]

The amount of charge that flows past a point in the wire during that time is approximately 26.8976 Coulombs.

Electric charge is quantized, meaning it exists in discrete amounts and is measured in coulombs (C). The elementary charge, represented by the symbol "e," is the charge of a single proton or electron, approximately equal to 1.602 x 10^-19 coulombs. Protons carry a positive charge, while electrons carry an equal but opposite negative charge.

When electric charges are stationary, they create an electric field around them. When charges are in motion, they produce a magnetic field in addition to the electric field, leading to electromagnetic effects.

Charge is a fundamental property of matter that determines its interaction with electric and magnetic fields and is crucial to understanding and explaining various electrical and electromagnetic phenomena in the natural world.

To calculate the amount of charge that flows past a point in the wire use the equation:

Q = I * t

Where:

Q is the charge (in Coulombs)

I is the current (in Amperes)

t is the time (in seconds)

Given:

Current (I) = 2.72 A

Time (t) = 9.88 s

Substitute these values into the equation to find the charge:

Q = I t

Q = 2.72 A * 9.88 s

Calculating the product:

Q = 26.8976 C

Therefore, the amount of charge that flows past a point in the wire during that time is approximately 26.8976 Coulombs.

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what is potential energy ​

Answers

Answer:

it is a type of energy with the formula of u=mgh

Explanation:

m means mass

g means gravitational field and

h means height

The energy an object has because of its position.

The small bunny exerts a force of 15 Newtons as it hops a distance of 3 meters to pass the large rabbit. How much work did the small bunny do?
45 Joules
0.2 Joules
18 Joules
5 Joules

Answers

Answer:

W = F × d

W = 15 × 3

W = 45 Joules

The fastest and longest skydive fell an amazing 19.5 miles. His average speed while falling was 254 mi/hr. How
much time did the dive last?
Need soon please!

Answers

Answer: 4.6 minutes

Explanation:

(254 mi/hr) x (1hr/60min)= 4.23 mi/min

(19.5mi) x (1min/4.23mi)= 4.6 minutes

When the fastest and longest skydive fell an amazing 19.5 miles. His average speed while falling was 254 mi/hr, then the dive lasted for 276.377 seconds

What is speed?

The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object. The unit of speed is meter/second. The generally considered unit for speed is a meter per second.

The mathematical expression for speed is given by

speed = total distance /Total time

As given in the problem The fastest and longest skydive fell an amazing 19.5 miles. His average speed while falling was 254 mi/hr

Total distance = 19.5 miles

Total time =?

average speed

By substituting respective values in the formula of speed

254 mi/hr = 19.5 miles/time

time = 19.5/254 hr

time = 0.0767716 hr

As we know 1 hr = 3600 seconds

0.0767716 hr = 0.0767716 ×3600 seconds

                       =276.377 seconds

Thus, the dive lasted for 276.377 seconds

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